If WM claims that not all of then are proper subsets of A, he should be able to prove that one of them is not a proper subset of A.

> It is clear that every possible sequence of naturals in A is> contained in a line of the table

It is not clear to me, or to anyone sensible, that the entire sequence of all naturals in A, which has no maximal member, is "in" any line of naturals that has a maximal member, and it is equally clear that every line does have a maximal member.

Any set of axioms is possible in mathematics, it is just that some sets of axioms are more interesting that others.

And for most mathematicians most of the time, a system allowing infinite sets is far more interesting than one rejecting them.

WM is perfectly free to investigate any axiom system he chooses, but has nether the right nor the power to impose it on anyone else.